Running at light speed

I found it interesting when i learned that no matter how fast you are travelling through space, you will alwys measure light to be travelling at the same speed. Then I thought of something:

What would happen in this situation.

There is a race. The two racers are me, wearing my "light speed" shoes that lets me run at the speed of light, and the other racer is light itself. Watching this race is the observer Karl.
The distance to run is a light minute. (ie the distance light travels in a minute).
Who wins the race?

This is what I think, and it seems kinda strange.
Karl sees both me and light travelling at the same speed and we both reach the finish line at the same time (in one minute).
On the other hand, I, the runner, know that i am running at the speed of light but while im running, i measure light to travel at light speed with respect to my frame of reference. So although the runner reaches the finish line 1 minute after the start of the race, light fininshes the race in a fraction of a second in the runner's point of view.

That's why you can't travel at the speed of light: if your travelling at the speed of light, it is impossible for light to travel at the speed of light with respect to you. In the contrary this is possible (and sensible) if you travel at a speed lower than that of light.

Let us say, instead that the runner is travelling at 90% of light speed.

Then the observer observes the runnertaking 1.11 minutes to reach the finish line, while light took 1 minute.

On the other hand, in the runner's point of view, he reaches the finish line in 1.11 minutes but light sped right past him at light speed and reached the finish line in much less than 1 minute.
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My point is that as the runner gets closer to light speed (he does not actually have to reach light speed), then the observations made by the runner and the observer regarding how long it took light to cross the finish line, seem to contradict eachother

On the other hand, in the runner's point of view, he reaches the finish line in 1.11 minutes but

No, he doesn't. For him the distance between start + finish lines is contracted, but the finish line still approaches him at 0.9c. He sees a distance of 0.435 light minutes between the two lines. So he observes the light completing the race in 0.435 minutes (about 26 seconds), and himself finishing in 0.484 minutes (about 29 seconds).

On the other hand, in the runner's point of view, he reaches the finish line in 1.11 minutes but light sped right past him at light speed and reached the finish line in much less than 1 minute.

That's false. The observer will always see his own clock running normally. What some other observer measures is irrelevant to him.

I sense that you have some misconceptions about how to figure time dilation. If you'd like to make the scenario precise (give me the distance of the track and so on), I can show you precisely what every observer will see.

...seem to contradict eachother

It only seems that way because you are mixing reference frames; in other words, you aren't working the problem properly.

In relativity theory, it is impossible for a material object to move at the speed of light. Therefore your paradox is impossible to set up in the first place.

I had a feeling when I read the original post that he'd get a barrage of "You can't move at light speed!", but the problem is posed in such a way that this is mainly a semantic point. The real confusion, as chroot says, is in the reference frames. You can look at it two ways:

1) The runner is moving at 0.9c relative to the stationary finish line. From the point of view of an observer waiting at the finish line, it does take 1.11 minutes for the runner to arrive and 1 minute for the light. However, moving clocks always run slower, so from the point of view of the runner, it takes less time to get there, both for him and for the light (0.484 and 0.435).
2) The runner is moving at 0.9c relative to the stationary finish line. From the point of view of the runner, the distance to the finish line (coming at him at 0.9c) is contracted to less than a light minute, so it takes less time than that to get there, both for him and for the light.

Either description is valid, though I'm not sure which is easier to think about. The key thing to remember is that time dilation and length contraction are complementary concepts. The constancy of the speed of light requires one in the presence of the other.

Either description is valid, though I'm not sure which is easier to think about. The key thing to remember is that time dilation and length contraction are complementary concepts. The constancy of the speed of light requires one in the presence of the other.

And don't forget the relativity of simultaneity--a lot of people get confused on these problems because they take into account Lorentz contraction and time dilation but they forget about (or don't know about) the fact that different frames define simultaneity differently.

And don't forget the relativity of simultaneity--a lot of people get confused on these problems because they take into account Lorentz contraction and time dilation but they forget about (or don't know about) the fact that different frames define simultaneity differently.

A good point and yet another reason why spacetime diagrams are the preferred means of understanding SR.

Staff: Mentor

I had a feeling when I read the original post that he'd get a barrage of "You can't move at light speed!", but the problem is posed in such a way that this is mainly a semantic point.

I thought this was pretty unambiguous:

Razor436 said:

Karl sees both me and light travelling at the same speed and we both reach the finish line at the same time (in one minute).
On the other hand, I, the runner, know that i am running at the speed of light [...]

OK, now I see that he rephrased his question later to 90% of light speed. I was fixating on the original question.

I'd like to ask another question to make sure I understand this topic well.

Lets imagine a similar race.
In this race, there are 10 runners. Runner1 runs at 10%lightspeed, Runner2 at 20% of lightspeed, .... Runner9 at 90% of lightspeed, and the 10th runner is light itself. And Karl is watching the race in the stands.
Here is the important part: The 9 runners and the observer Karl are to raise a flag they have with them (a signal) when they see light cross the finish line.

Lets see if i understand this: I think all runners and the observer will disagree on how much time it took light to cross the finish the finish line and how much distance the light had to travel to reach the finish line. However, The 9 runners and the observer will raise their flags simultaneously.
Do i have that right?

However, The 9 runners and the observer will raise their flags simultaneously.
Do i have that right?

Remeber what JesseM said? Simultaneity is defined different in different frames. So there is no meaning in your statement (as long as you don't mention according to who the flags are raised simultaneously).

Remeber what JesseM said? Simultaneity is defined different in different frames. So there is no meaning in your statement (as long as you don't mention according to who the flags are raised simultaneously).

And if each runner raises his flag when he sees the light cross the finish line in his own frame, then in each runner's own frame all the other runners will raise their flags at different times.

Imagine this situation.
There is a car race. The car we are interested in travels at 90% lightspeed. To this car is attached a camera so we kinda have a view of what the driver sees (like in a car race on TV). The videa from the camera is broadcast live on TV.
An observer is at the race in person and also has a TV next to him, watching the footage from the camera on the car.
In the observer's frame, does he see the car cross the finish line first in real life or on tv or do they happen at the same time?

It depends on the path the TV signal takes. Does the signal go from the camera directly to the observer at the race - or does it go to the TV truck, then to the broadcast studio (possibly via a satellite link), then back to the viewer?

If the TV signal takes a direct path, they both should arive at about the same time, as the TV signal travels as the same speed that light does. If the TV signal takes an indirect path (very likely), it will arive later than the light.

Note that what a person sees is not the Lorentz transformation, but the Lorentz transformation plus associated speed-of-light signal delays. Search some of the past physics forum threads for "Terrel rotation" for some of the technical details of what an observer sees. There's a website which has educational videos which show what sort of visual relativistic effects an observer would see if the speed of ligh were very slow (you can also think of this as what an actual observer would see if he played the video back in slow-motion, as watching someone travel a mile travelling at 90% of the speed of light takes 5 microseconds, not enough time to enjoy the show.

Funny, my thought experiments DO let me run this fast. It's just
that they can never become physical experiments.

Albert Einsten had this very thought experiement when he was coming up
with special relativity (only he thought of trains instead of tennis shoes.)

What chroot means is that (in special rleativty) it is not just practically impossible, but theoretically impossible, so the only thing that physics tells us about running at light speed is that we can't do it.

If you want to make a thought experiment about running faster than light, you're ipso facto no longer working with special relativity, which is the mainstream theory describing high-velocity motion, because running faster than light is not possible in that theory.

If you're no longer working with special relativity, who knows what theory/model you're working with? It could be anything at all, as fanciful as you like -- but then your question still has no definite answer, and the discussion doesn't belong on this site, anyway.